Instantaneous radiopositioning using signals of opportunity

ABSTRACT

Instantaneous radio positioning method and system. Signals from a plurality of spatially distributed transmitters are received at a known reference position and at an unknown position to be determined. A composite of the radio signals, simultaneously including a component signed from each of the transmitters, is digitized and then processed to measure phases that is then digitized. Ambiguity is resolved by finding the location in parameter space of the maximum of an ambiguity function related to sets of phase-measurement data. Position is determined at a point in time without keeping track of phase history.

[0001] The U.S. Government has rights in this invention pursuant to AirForce Contract number F19628-00-C-0002 awarded by the Air Force'sElectronic Systems Center, Hanscom AFB, Mass.

1. BACKGROUND OF THE INVENTION

[0002] 1.1. Field of the Invention

[0003] This invention relates to improved techniques for determiningposition by radio, more particularly for determining positioninstantaneously, from carrier-wave phases of radio signals received fromtransmitters having different carrier-wave frequencies. In a preferredembodiment of the invention, these carrier waves also have randomphases, and the position of a receiver is determined by reference to thephases of signals received by another, reference, receiver. Theinvention includes resolving, or reducing, the position ambiguitystemming from the integer-cycle ambiguity inherent in an observation ofthe phase of a periodic wave such as a carrier wave. Resolving ambiguityenables practically instantaneous position-determination, which is asubstantial improvement over prior-art techniques based on sustained,continuous, carrier phase tracking.

[0004] 1.2. U.S. Pat. No. 4,667,203; GPS; GLONASS

[0005] In U.S. Pat. No. 4,667,203 one of the present inventors(Counselman) discloses methods and systems for determining position fromcarrier-wave phases of radio signals received from a plurality oftransmitters aboard earth-orbiting satellites such as those of theGlobal Positioning System (GPS). The disclosure of Counselman '203includes methods and systems for resolving position ambiguity caused bythe integer-cycle ambiguity of carrier phase. In a preferred embodimentof Counselman '203, the transmitted signals have random phases, and theposition of a receiver is determined by reference to the phases ofsignals received at another, reference, receiver. However, Counselman'203 requires the transmitted signals to have suppressed carriers and/orwide, overlapping, spectra.

[0006] Counselman '203 does not teach or render obvious a technique fordetermining position from carrier waves transmitted with differentfrequencies. Counselman '203 does not teach or render obvious aninstantaneous positioning technique. On the contrary, Counselman '203teaches determining position by combining observations spanning asignificant period of time, such as several thousand seconds.

[0007] In the Russian GLONASS system, which is otherwise very similar toGPS, different satellites transmit signals with slightly differentimplicit carrier frequencies. (Both the GLONASS and the GPS satellitestransmit substantially overlapping spread-spectrum signals whosecarriers are actually suppressed.) These slight carrier-frequencydifferences are intended to facilitate the separation of differentsatellites' signals in a receiver. An instantaneous radiopositioningmethod using combined GPS and GLONASS observations that includesresolving implicit carrier-phase ambiguities despite the GLONASSfrequency differences is disclosed in a paper entitled “Single-epochinteger ambiguity resolution with GPS-GLONASS L1 data,” by M. Pratt etal., appearing in the Proceedings of the Institute of Navigation AnnualMeeting in Albuquerque, N. Mex. June 1997, pp. 691-699.

[0008] 1.3. Mites

[0009] In an article entitled “Miniature Interferometer Terminals forEarth Surveying (MITES)”, appearing in Bulletin Geodesique, Volume 53(1979), pp. 139-163, by Charles C. Counselman III. and Irwin I. Shapiro,there is proposed a system for determining position by measuringcarrier-wave phases of multi-frequency radio signals received from aplurality of earth-orbiting satellites. The reason for having multiplefrequencies is to resolve ambiguity and determine positioninstantaneously. However, the MITES scheme requires each one of theplurality of transmitters to emit the same multiplicity ofdifferent-frequency carrier waves. (Small frequency shifts and/ormodulation are used to mitigate interference, as in the above-mentionedGLONASS system.) In other words, although Counselman and Shapiro teachthe use of multiple frequencies, they teach that the multiplefrequencies must be transmitted by each single transmitter; and that alltransmitters should transmit the same frequencies.

[0010] 1.4. Differential Measurements

[0011] The idea that all transmitters utilized in a radio-positioningtechnique should transmit the same or nearly the same frequencies isfundamental to many radiopositioning systems, including Loran and Omega(discussed below) in addition to GPS, GLONASS and MITES (discussedabove). It is desired for all transmissions to be the same frequencyband, or “channel,” not merely to conserve spectrum, but fundamentallyto facilitate differential measurements, i.e., measurements ofdifferences between signals received from different transmitters.

[0012] 1.5. Loran

[0013] The Loran system is described in an article by W. O. Henry,entitled “Some Developments in Loran,” appearing in the Journal ofGeophysical Research, vol. 65, pp. 506-513, February 1960. The currentversion of Loran, known as Loran-C, employsseveral-thousand-kilometer-long chains of synchronized transmittersstationed on the surface of the earth, with all transmitters having thesame implicit carrier frequency, 100 kiloHertz, but with eachtransmitter emitting a unique time-sequence of short pulses. Thissequence, which includes polarity reversals of the pulses, enables areceiver to distinguish between signals from different transmitters. Asuitable combination of observations of more than one pair oftransmitters can yield a determination of the receiver's position on thesurface of the earth. Basically, a receiver observes the differencebetween the times of arrival of pulses from a pair of transmitters.Since the transmitters are synchronized, a time-difference-of-arrival(TDOA) observation implies that the receiver is located somewhere alonga particular hyperbolic curve having vertices at the transmitters. (Thelocus of points having a given difference between their distances fromtwo vertices is an hyperbola.) Observing TDOA for additional pairs oftransmitters provides additional hyperbolic constraints on thereceiver's position, and enables a unique position to be determined.

[0014] 1.6. Omega

[0015] The Omega system is described in an article by Pierce, entitled“Omega,” appearing in IEEE Transactions on Aerospace and ElectronicSystems, vol. AES-1, no.3, pp. 206-215, December 1965. Omega, like Loranand conventional GPS, is an hyperbolic positioning system. In the Omegasystem, the phase difference between the radio waves received fromdifferent transmitters is measured rather than (principally) the timedifference (TDOA) as in the Loran-C system. To facilitate resolution ofphase ambiguity, Omega transmitters transmit plural frequencies.However, different transmitters transmit the same frequencies. Again,this is done to facilitate differential measurements.

[0016] 1.7. Utilizing Signals of Opportunity

[0017] It is known in the radiopositioning art, i.e., the art ofdetermining position by radio, to utilize signals of opportunity, bywhich we mean signals emitted by uncooperative transmitters. Typicallysuch transmissions are not intended for positioning; differenttransmitters operate on wholly different frequencies; they are notsynchronous; and their carrier-wave phases are random. Lack ofsynchronization or instability in time, frequency, and/or phase preventsmany radiopositioning methods from being usefully employed.

[0018] An example of radiopositioning by utilizing signals ofopportunity is determining position by radio direction finding (RDF)observations of commercial broadcast signals in the medium-frequency,amplitude-modulated (AM) broadcast band from about 550 to 1700 kHz.These signals are transmitted for purposes other than positioning, butthe transmitters are marked and identified on nautical charts tofacilitate their use as radio beacons, for navigation by RDF. DifferentAM broadcast transmitters within any given region of the country (orworld) are assigned to completely separate, disjoint, frequency channelsto avoid interference.

[0019] Another prior-art radiopositioning technique utilizing signals ofopportunity tracks the phases of the carrier waves of signals receivedfrom commercial broadcasters in the medium-frequency AM broadcast band.By “tracking the phase of the carrier wave of a signal” we meancontinuously or effectively continuously measuring the phase of thecarrier wave with respect to a local reference oscillator; and keepingtrack of the time-variation of the measured phase from an initial timewhen the receiver's position was known, to a later time when theposition is unknown and to be determined. Continuity of tracking isessential. If tracking were interrupted, the phase change during thehiatus would be unknown, so later positions could not be determinedwithout resort to external information. This problem is discussedfurther in the following section.

[0020] In an article entitled “The CURSOR Radio Navigation and TrackingSystem,” by Peter J. Duffett-Smith et al., appearing in the Journal ofNavigation, vol. 45, no. 2, May 1992, pp. 157-165, an AM-broadcast-bandcarrier phase tracking system called “CURSOR” is described and thestatement is made, “A drawback of a phase-measuring CURSOR system is itsneed to track the signals continuously from each radio transmitter. Inmany applications this is not a problem, but when used for vehicletracking in cities there are always heavily-shadowed regions such astunnels, underpasses, and petrol-station forecourts where the signalsbecome too weak to track or disappear altogether. When the vehicleemerges from the shadow, the receivers lock themselves back on to thesignals, but there is now an uncertainty equal to an integer number ofwavelengths in the measured phases from each transmitter. Hence, the . .. [vehicle's] true position is no longer known. However, by using manymore than the minimum three channels [i.e., broadcast stations], thesolutions to the equations are constrained to the extent that only oneof them is usually physically possible.” (Op cit., at the bottom of page163 and top of page 164.)

[0021] Thus, Duffett-Smith et al. disclose that phase-ambiguity can beresolved. Their method is not disclosed in enabling detail. It alsoseems not to have worked well for them, because they state (in theparagraph beginning at the middle of page 164), “A further drawback of aphase-measuring CURSOR system is the need to calibrate the systemagainst known positions from time to time.” Such recalibration isrequired in a phase-tracking system if only changes in position arebeing determined, from changes in phase, without an ability to determineposition at any single time, i.e., instantaneously.

[0022] 1.8. Instantaneous vs. Incremental Positioning

[0023] “Tracking” methods such as the one described by Duffett-Smith etal. are intrinsically incapable of instantaneous positioning. By“instantaneous positioning” we mean determining position at an instant,i.e., at a single point in time, as opposed to determining how aposition has varied during the extended time interval since continuoustracking began, or last resumed. Tracking is an “incremental”positioning technique, as opposed to an instantaneous positioningtechnique.

[0024] Instantaneous positioning is advantageous, in comparison withincremental positioning, because tracking is subject to beinginterrupted for many reasons, including both deliberate and accidentalreasons. An example of a deliberate reason is to conserve energy bykeeping receiver power turned off until a position determination isrequired. This reason is important for battery-powered equipment. Anexample of an accidental interruption is that a vehicle carrying atracking receiver enters a tunnel. Another, serious, disadvantage ofincremental positioning is that errors are cumulative.

[0025] It is known to combine instantaneous and incrementalradiopositioning techniques. For example, in an article entitled“Synergism of Code & Carrier Measurements,” by Ron L. Hatch, appearingin the Proceedings of the Third International Geodetic Symposium onSatellite Doppler Positioning, pp. 1213-1231, Feb. 8-12, 1982, LasCruces, N. Mex., a method of combining incremental position informationderived by carrier-phase tracking, with instantaneous positioninformation derived from “code” time-of-arrival measurements, isdisclosed. Combining instantaneous and incremental positioningtechniques may be advantageous when, as in the case described by Hatch,the incremental technique is more precise than the instantaneoustechnique.

[0026] By “position information” we mean data relating to position, fromwhich position may be determined. An example of position information isTDOA measurement data. Another example of position information iscarrier-phase measurement data. Position, per se, is usually expressedin position coordinates such as latitude and longitude, or northing andeasting, relative to some origin or reference.

[0027] 1.9. Reciprocity

[0028] Most radiopositioning techniques, including those of the presentinvention, may be “turned around”; i.e., one may determine the positionof a transmitter, instead of or in addition to, the position of areceiver, from measurements of received signals. In relative-positioningtechniques, such as in the present invention, determining the positionof one receiver relies on having position information from a secondreceiver. This determination may be performed by combining data fromboth receivers at either receiver, or in a third place.

2. SUMMARY OF THE INVENTION

[0029] It is a general object of the present invention to provideimproved techniques for determining position, or navigating, by radio.

[0030] A further object of the present invention is to provide improvedtechniques for instantaneous radiopositioning.

[0031] A more specific object is to provide improved techniques forradiopositioning utilizing radio signals received from differenttransmitters having, respectively, different frequencies.

[0032] A still more specific object is to provide improved techniquesfor radiopositioning utilizing radio signals received from differenttransmitters having random phases.

[0033] A specific object is to provide improved techniques fordetermining position by utilizing radio signals “of opportunity,” i.e.,signals emitted by uncooperative transmitters.

[0034] Yet another more specific object of the present invention is toprovide improved techniques for resolving or reducing ambiguity indetermining position by radio.

[0035] In a first aspect, the invention which achieves the foregoingobjects, is a method of instantaneously determining an unknown positionusing radio signals from a plurality of transmitters having widelydistributed and known positions and a wide range of radio frequencies.The method includes measuring the phases of the radio signals arrivingconcurrently at an unknown position to obtain a first set ofphase-measurement data. The phases of radio signals arrivingconcurrently at a known reference position is measured almostsimultaneously with their arrival at the unknown position to obtain asecond set of phase-measurement data. The first and second data sets arecombined to determine the unknown position.

[0036] In a preferred embodiment the radio signals arrive at the unknownposition via ground-wave propagation from the plurality of transmitterswhich operate independently and whose radio signals are transmitted withrandom phases. In another embodiment, the first set of phase measurementdata refers to a first instant of concurrent-signal-arrival at theunknown position and the second set of phase-measurement data refers toa second instant of concurrent-signal-arrival time at the referenceposition, and the departure from simultaneity of the first and secondinstants is determined simultaneously with the determination of theunknown position. It is preferred that position ambiguity be resolved byestablishing an ambiguity function and finding the location of themaximum of the ambiguity function.

[0037] In another aspect, the invention is a radiopositioning system forinstantaneously determining an unknown position. The system includes aplurality of spatially distributed transmitters at known locations, thetransmitters transmitting signals at widely distributed frequencies. Afirst receiver is located at the unknown position and is adapted toreceive the signals from the plurality of transmitters and to determinethe phases of the signals at the unknown position to generate a firstset of phase-measurement data. A second receiver is located at a knownreference position adapted to receive the signals from the plurality oftransmitters and to determine the phases of the signals at the knownreference position to generate a second set of phase-measurement data.Computer apparatus operates on the first and second sets ofphase-measurement data to determine the unknown position. In a preferredembodiment, the computing apparatus is programmed to find the locationin parameter space of the maximum of an ambiguity function of the setsof phase-measurement data, the location of the maximum being the unknownposition. It is preferred that the ambiguity function be a sum, over allof the transmitters, of a periodic function of the phase-measurementdata. It is also preferred that the periodic function have a period ofone phase cycle. Other appropriate functions are disclosed hereinbelow.It is also preferred that the output of the first and second receiversbe a composite signal that is then digitized for processing.

3. BRIEF DESCRIPTION OF THE DRAWINGS

[0038]FIG. 1 is a schematic representation of a part of the earthincluding several fixed radio transmitters, a fixed reference station,and a vehicle bearing a radio receiver, whose position is to bedetermined.

[0039]FIG. 2 is a block diagram showing in more detail system componentslocated at the fixed reference station shown in FIG. 1.

[0040]FIG. 3 is a block diagram showing in more detail system componentslocated at the vehicle shown in FIG. 1.

[0041]FIG. 4 is a block diagram showing components of the receiverlocated at either the fixed reference station or the vehicle.

[0042]FIG. 5 is a block diagram showing components of input-protectioncircuitry within either receiver.

[0043]FIG. 6 is a block diagram showing components of a calibrationsignal generator within either receiver.

[0044]FIG. 7 is a plot of an ambiguity function which is maximized todetermine instantaneous position.

[0045]FIG. 8 is a plot of the same ambiguity function as FIG. 7, butover a 100-times-greater area.

[0046]FIG. 9 shows a plot of the same ambiguity function, over the same100-square-km area as FIG. 8, but with a slightly incorrect assumptionregarding clock synchronization.

[0047]FIG. 10 is a scatter plot of positions determined in ashort-distance demonstration of the invention.

[0048]FIG. 11 is a plot, versus time, of positions determined in ashort-distance demonstration of the invention.

[0049]FIG. 12 is a plot showing values of individual cosine terms in themaximized ambiguity functions for the short-distance demonstration.

[0050]FIG. 13 is a plot showing instantaneous-positioning results from alonger-distance demonstration of the invention.

[0051]FIG. 14 is a graph showing results from the longer-distancedemonstration plotted versus time.

[0052]FIG. 15 is a graph showing periodic functions used in analternative ambiguity-function embodiment.

[0053]FIG. 16 is a block diagram showing a repeater enabling aradiopositioning antenna and receiver to be located away from theirassociated computer system.

4. DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0054]FIG. 1

[0055] Referring now to FIG. 1, there is shown (schematically, not toscale) a part of the earth's surface 10 and a plurality of subsurfacelayers 12, 16, 20 with interfaces 14, 18. Layer 12 could beunconsolidated soil; layer 16 could be dry rock; and layer 20 could berock saturated by water. Interface 18 in this example would be theso-called water table.

[0056] In general these layers will have different electricalproperties, characterized for example by different complex dielectricconstants. These layers may or may not be uniformly thick throughout ageographic region; in other words, their interfaces 14, 18 may or maynot be horizontal.

[0057] At various fixed and known locations in the geographic regionshown in FIG. 1 are a plurality of radio transmitters, of which arepresentative set of six transmitters 30-1, 30-2, 30-3, . . . 30-6 areshown. In the preferred embodiment these are amplitude modulated (AM)broadcast transmitters operating in the AM broadcast band of frequenciesfrom about 530 kHz to about 1700 kHz. Each transmitter has a uniquecarrier frequency, so its signal is readily distinguishable byfrequency-selectivity in a receiver. The carrier is explicitly presentin the signal as a continuous-wave component. On both sides of thecarrier in the frequency domain are sidebands created by the amplitudemodulation. In the United States, carrier frequencies are assigned bythe Federal Communications Commission (FCC) and are constrained to bewhole-number multiples of 10 kHz, with a tolerance of ±50 parts permillion. The sidebands are limited to about ±5 kHz. In some othercountries, carrier frequencies are assigned on 9-kHz multiples, and thebandwidth occupied by sidebands may be narrower. Generally thetransmitters within a region are assigned to non-overlapping frequencychannels to avoid interference.

[0058] The transmitters drive vertical antennas with respect to ground.The region of reception and utilization of their signals (not drawn) ispreferably limited to a distance of several tens of kilometers. Withinthis region the signals propagate primarily in the so-called “groundwave” mode, which is predominantly vertically polarized. So-called “skywave,” or ionospherically reflected, signal components are relativelyinsignificant within this region, even at night when the ionosphere isnot strongly absorbing. A ground-wave signal propagates radially outwardhorizontally from each transmitter 30. Wavefronts of the carrier-wavecomponent of each said signal (not drawn) are essentially circular,centered on the transmitting antenna. The ground wavelength, i.e., thehorizontal distance between wavefronts differing in phase by one cycle,is nearly equal to the speed of light in vacuum, c, divided by therespective carrier frequency in Hz. The precise wavelength depends onthe detailed electromagnetic properties (mainly the conductivity andpermittivity) and thicknesses of subsurface layers 12, 16, 20. Formulasand procedures for calculating the ground wavelength are known and arereadily available in the technical literature of radio-propagation,e.g., in the IEEE Transactions on Antennas and Propagation, published bythe Institute of Electrical and Electronics Engineers, New York, circa1999. However, for most practical purposes, over distances of the orderof kilometers, it is sufficient to adopt the vacuum wavelength. Ifnecessary, more exact values of ground wavelength may be determined bytraversing the region and simultaneously measuring ground-wave phases(e.g., as disclosed herein) and position, position being determined byindependent means such as GPS.

[0059] Also within the geographic region shown in FIG. 1 are a fixedreference station 40 and a vehicle 50. The location of fixed referencestation 40 is known. The location of vehicle 50 is unknown and to bedetermined. It will be determined by reference to data fromcarrier-phase measurements at fixed reference station 40. In principle,reference station 40 could also be a moving vehicle. In this case,independent means such as GPS could be used to determine its position atany time. Also in principle, if reference station 40 and vehicle 50 werewidely separated, it would be possible to determine the positions ofboth simultaneously by extending the techniques of the presentinvention. However, simultaneous estimation of two unknown positionsrather than one would require substantially more computing time toresolve ambiguity, and is therefore not preferred.

[0060] It would be a straightforward matter to utilize data from aplurality of reference stations similar to reference station 40 todetermine the position of vehicle 50. This would be preferred, forexample, if it could occur that vehicle 50 drove out of range of onereference station 40. An extensive geographical area might be served byan extensive network of reference stations 40.

[0061] In the preferred embodiment of the invention, data aretelemetered from reference station 40 to vehicle 50. In a non-real-timeversion of the invention, means for telemetering data between referencestation 40 and vehicle 50 are omitted, and data from both are stored andcombined for processing later, e.g., after vehicle 50 has returned toreference station 40.

[0062] As shown in FIG. 1, reference station 40 has a vertical antenna42 adapted for receiving the ground-wave signals from transmitters 30.Reference station 40 also has a transmitting antenna 44 adapted fortransmitting data to vehicle 50. Vehicle 50 has a vertical antenna 52adapted for receiving the ground-wave signals from transmitters 30, andalso an antenna 54 for receiving data from antenna 44 at referencestation 40.

[0063] A skilled radio practitioner knows how to multiplex an antena anduse it simultaneously for both transmitting and receiving, or forreceiving multiple signals, in very different frequency bands,simultaneously. Thus, for example, antennas 42 and 44 could convenientlybe combined; and antennas 52 and 54 could conveniently be combined.Reference station 40 could also be merged with a transmitter 30. Aplural subset of the plurality of transmitters, e.g., transmitters 30-1and 30-2, could be merged. In other words, two or more signals, withdifferent carrier frequencies, could be transmitted from one antenna 30.This is in fact a common practice in the United States.

[0064] Preferably the transmitters 30 are located in a wide range ofdirections as viewed from vehicle 50 and antenna 52; ideally, thetransmitters more or less surround vehicle 50 and antenna 52. However,it is not important for the transmitters to be uniformly distant oruniformly spaced azimuthally (i.e., around the horizon). Preferably, thedifferent frequencies of these transmitters span a wide range offrequencies, and have a wide range of spacings from narrow to wide.Preferably, the transmitter frequencies are distributed substantiallyindependently of the transmitter positions. For example, it would beundesirable for all of the lower-frequency transmitters to be in onedirection, and all of the higher-frequency transmitters to be in anorthogonal direction. These are general and somewhat “soft” preferences.In practice, the distribution of AM broadcast stations around a typicalU.S. metropolitan area is satisfactory. If the distribution were poor,this would be evident in the appearance of the “ambiguity function” tobe described hereinbelow. If the distribution were very poor it could beremedied by placing supplementary, low-power, unmodulated,continuous-wave transmitters within the region of interest.

[0065] Often an AM broadcast station has an antenna comprising aplurality of towers operating as elements of a directional arrayantenna. That is, each tower of the array is excited with the samefrequency, but different amplitudes and phases so as to form a beam ofradiation or to avoid radiating in a particular direction. For thepurposes of the present invention these multiple towers may be treatedseparately or they may be represented by a single-point antenna at thephase-center of the array. The latter method is satisfactory ifreceiving sites 40 and 50 are in the far field of the array.

[0066]FIG. 2

[0067] Now referring to FIG. 2, the components of our preferredembodiment located at reference station 40 are seen. Station 40 includesan antenna 42 connected to a receiver 43 for receiving the signals fromall of the plurality of transmitters 30-1, 30-2, 30-3, . . . 30-6, etc.,simultaneously. simultaneously. Receiver 43 applies a composite of allof these simultaneously received signals to ananalog-to-digital-converter unit 45 such as the model PCI-416D2 made byDatel, Inc., Mansfield, Mass. This unit plugs into the standard PCI bus46 of an Intel-based personal computer, or “PC,” 47. Computer softwareand data are stored in memory 48 which is preferably a hard-disk drive.A software package, Datel PCI-416NTS, running under a Microsoft Windowsoperating system on computer 47, drives analog-to-digital-converter unit45. Included in unit 45 are a crystal oscillator 453 which governs thesampling frequency of analog-to-digital-converter 451 and the rate ofclock 452 which controls when sampling starts and stops. The samplingfrequency and the start and stop times are set via the driver softwarerunning in computer 47. The entire AM broadcast band is digitizeddirectly (without downconverting) at 5 Million samples per second, with12 bits per sample.

[0068] Subsequent radio signal processing and measurement functions areperformed via software in computer 47. In our preferred mode ofoperation, a burst of 2²² (about 4 Million) samples is taken andprocessed every five seconds. The 2²² length data burst spansapproximately 0.8 second. The computer performs a 2²² length FastFourier Transform (FFT) of this time-series of samples. The resultingcomplex-amplitude spectrum has resolution of about 1.2 Hz. The magnitudeof this spectrum is searched in the vicinity of the assigned frequenciesof the AM broadcast stations 30 to find the very narrow peakscorresponding to the carrier waves transmitted by these stations. Byinterpolation of the points on each peak, the frequency, phase, andmagnitude of each carrier signal is estimated. The estimated carrierfrequency is simply the frequency of the interpolated peak magnitude ofthe Fourier transform. The estimated phase and magnitude are simply theangle and the magnitude of the complex amplitude of the Fouriertransform at this frequency. These estimates, which we call “measurementdata,” are stored in memory 48, tagged with the time of the sample-burstas indicated by clock 452.

[0069] These time-tagged-measurement data are transmitted by telemetrytransmitter 41 in near real time, with as little latency as possible.Included with the measurement data in this transmission areposition-coordinate data representing the (known) positions of alltransmitters 30 and of the reference station 40. The latter data areread from memory 48 by computer 47 and merged with the localreceived-carrier-measurement data; and the composite data message isapplied by computer 47 via line 49 to transmitter 41.

[0070] In summary: at reference station 40 the amplitudes, frequencies,and phases of the carrier waves received from all available transmitters30 are measured at times governed by clock 452; and the time-taggedmeasurement data are transmitted via transmitter 41 and antenna 44 tovehicle 50.

[0071]FIG. 3

[0072] In FIG. 3, system components located at vehicle 50 are seen.Vehicle 50 includes an antenna 52 for receiving the signals transmittedby all transmitters 30-1, 30-2, 30-3, . . . 30-6, etc., and an antenna54 for receiving the data transmission from reference stationtransmitter 41 shown in FIG. 2. Vehicle antenna 52 should beelectromagnetically similar, and preferably is identical, to referencestation antenna 42 shown in FIG. 2. As mentioned, a single antenna maybe multiplexed to perform the functions of both vehicle antennas 52 and54.

[0073] The signals sensed by antenna 52 are applied to receiver 53 whichshould be similar, and preferably is identical, to reference stationreceiver 43 shown in FIG. 2. Similarly, vehicle 50 is equipped withanalog-to-digital-converter unit 55 which is likeanalog-to-digital-converter unit 45 shown in FIG. 2.Analog-to-digital-converter unit 55 includes analog-to-digital-converter551, clock 552, and oscillator 553 which are like their counterparts451, 452, and 453 shown in FIG. 2. Again similarly, vehicle 50 isequipped with a computer 57, bus 56, and memory 58, which are like theircounterparts 47, 46, and 48 shown in FIG. 2. However, instead of atelemetry transmitter and antenna, vehicle 50 is equipped with atelemetry receiver 60 and antenna 54.

[0074] If desired, both a telemetry transmitter and a telemetry receivercould be included at each location 40 and 50. In this case, it would bepossible at either site to determine the unknown position(s).

[0075] Computer 57 is equipped with an output device 61, such as a videodisplay, for displaying position-determination results.

[0076] For the signal received from each transmitter, vehicle receiver53, analog-to-digital-converter unit 55, and computer 57 and itsperipherals operate to measure, exactly as their counterparts atreference station 40 do, the amplitude, frequency, and phase of thecarrier wave received from each of the plurality of transmitters 30. Theresulting measurement data, time-tagged at vehicle 50 with thesample-burst times indicated by clock 552, are stored in memory 58. Inour preferred mode of operation, this is done every five seconds atvehicle 50, just as it is done at reference station 40. However, eachfive-second sampling “epoch” stands on its own, and position isdetermined at each such epoch “instantaneously,” without needing datafrom any other epoch. There is no requirement for continuous tracking ofthe carrier signals.

[0077] The sampling epochs occur preferably on integer minutes and at 5,10, 15, . . . seconds thereafter. Computer 57 approximately synchronizesitself and clock 552 with the computer 47 and clock 452 at the referencestation via the telemetry transmission it receives via antenna 54 andtelemetry receiver 60. This synchronization is inexact, but is easilykept within less than 100 microseconds, or the time required for a radiosignal to travel about 30 km.

[0078] In addition to the measurement functions just mentioned, computer57 performs the numerical and logical calculations necessary todetermine the position of vehicle 50 with respect to the known positionof reference station 40 shown in FIG. 2. The details of thesecalculations are given below in the section entitled “Computation ofinstantaneous position” and in several following sections. Because ofthis additional computing burden, if a new position determination willbe desired for every five-second epoch, vehicle 50 should be equippedwith more computing “horsepower” than reference station 40, where (inour preferred embodiment) no position computation is done.Alternatively, a position may be computed less often in real time,and/or measurement data may be accumulated and processed later.

[0079]FIG. 4

[0080] In FIG. 4 are seen the components of receiver 43, which is shownin FIG. 2. Receiver 53, shown in FIG. 3, is preferably identical.Antenna 42 is connected to protective circuit 62 which protects thefollowing circuits of the receiver from being damaged if a powerfultransmitter operates near antenna 42. Protective circuit 62 alsoreceives a receiver-calibration signal from calibration signal generator63. The signals received by antenna 42 plus this receiver-calibrationsignal are amplified by a buffer amplifier 64, such as Analog Devicesintegrated-circuit type BUF04, then filtered by a band-limiting filter65. This filter provides anti-aliasing for the subsequent 5 M/secondsampling by analog-to-digital-converter 451 shown in FIG. 2. In ourpreferred embodiment, filter 65 is a eight-pole Butterworth low-passtype with a cutoff frequency of 2 MHz, made by Allen Avionics, Inc.,Mineola, N.Y. However, a simpler filter could be substituted.

[0081] The output of filter 65 is amplified by variable-gain amplifier66, whose output is applied to analog-to-digital-converter 451 shown inFIG. 2. In our preferred embodiment, amplifier 66 uses a cascade ofthree Analog Devices type AD844 integrated-circuit high-speedoperational amplifiers, each with its feedback resistor switched by areed relay, or two. The voltage gain of each of the first two stages canbe switched to either 1 or 4, and the gain of the third stage can beswitched to 1, 2, 4 or 8. Thus the gain can be varied in 6-dB steps overa range of about 42 dB. The gain-control relays are switched in responseto peak detector 67 which measures the peak absolute value of the outputof amplifier 66. The gain control operates to keep the peak absolutevalue of the voltage applied to analog-to-digital-converter 451 within±3 dB (a factor of 0.7 to 1.4) of 1 volt. The saturation voltage of theconverter is ±2.5 volts. The gain is switched in between samplingbursts.

[0082]FIG. 5

[0083] In FIG. 5 the components of protective circuit 62 are seen. Theantenna 42 is connected to one terminal of a neon lamp bulb 70, such asChicago Lamp type C2A, whose other terminal is connected to receiverground 71. The antenna 42 is also connected through a small fast-actingfuse 72, such as Littlefuse type 273125, and a 500-ohm, 30-watt resistor73 such as Caddock type MP930, to the input of buffer amplifier 64. Thevoltage input to buffer amplifier 64 is limited by fast, low-capacitancediodes 74-1 and 74-2, such as Motorola type MBD701, connected topositive and negative 15-volt buses 75 and 77, respectively. Thisprotective circuit is very robust, yet it loads the input of amplifier64 with very little capacitance.

[0084] As mentioned, a receiver-calibration signal from calibrationgenerator 63 is also applied to protective circuit 62. This signal comesvia 50-ohm coaxial cable 91, which is terminated by 51 -ohm resistor 68.The signal is coupled to the input of amplifier 64 via 10-pf capacitor69.

[0085]FIG. 6

[0086] In FIG. 6, the components of calibration generator 63 are seen. Asine-wave signal from a 10-MHz crystal oscillator 80 is amplified andclipped by a voltage comparator 81, such as Linear type LT1016, toproduce a square-wave, logic-level, signal 82, which is divided infrequency by a factor of 498 in divider 83. Divider 83 is a synchronizedflip-flop cascade configured as a preset counter, preferably assembledfrom MC74AC109 and 74AC161 integrated circuits. The frequency that itgenerates, equal to 10 MHz divided by 498, or about 20080.321285 Hz, isincommensurate with the 10-kHz carrier-frequency spacing, so harmonicsof this signal do not interfere with carrier phase measurement.

[0087] The square-wave output of divider 83 is coupled to the base of abipolar junction transistor 84, such as Motorola type MMBR901LT1, by a33-pf capacitor 85. The transistor base is also connected to ground 87through a 33-ohm resistor 86. This RC circuit acts as a differentiatorso that the transistor 84, normally biased off, is switched on for avery short time, of the order of a few nanoseconds, by thepositive-going transitions of the divider 83 output. The collector ofthe transistor is connected to a +5 volt supply 89 by a 100-ohm resistor88. The very short pulses appearing at the collector are coupled tocoaxial cable 91 through a 51-ohm resistor 90. Cable 91 carries the20080.321285-Hz impulse train to the receiver-input protective circuit62.

[0088] The spectrum of this impulse train is a comb of impulses, orharmonics of 20080.321285 Hz, in the frequency domain. The FFT-basedsoftware running in computer 47 detects and measures the phases of theseharmonics just as it measures the broadcast-station carriers.

[0089] For calibration of the receiver it is not necessary to know thephase or the exact frequency of oscillator 80, because the phase of thisoscillator appears as a pure time delay in the spectrum of thecalibration signal. A time delay of the receiver is completely absorbedin the estimate of the sampling-clock synchronization error that is madein the course of position estimation, as described below. A time delayappears as a linear phase-vs.-frequency characteristic. Only thedeparture from linearity is important.

[0090] In practice we find that the receivers that we constructed asdescribed above are so nearly identical that phase calibration isunnecessary. Phase calibration could easily become important, forexample if simpler filter and amplifier circuits were substituted or ifthe two receivers had different designs. Phase calibration could also bemore important if a repeater were used as discussed below in relation toFIG. 16. In any case, the phase calibrator is useful as a test signal.

[0091] Computation of Instantaneous Position

[0092] We now describe, with the aid of detailed mathematical formulas,the computation which completes an instantaneous position determination.

[0093] As already described, at convenient epochs (e.g., every fiveseconds on the zeros and fives) the phase, frequency, and amplitude ofeach received carrier signal are measured for all observabletransmitters at reference station 40, whose position is assumed known.In the following we will refer to this station as the “base,” and informulas we will designate it by a subscript b. Similarly, allobservable carrier signals are measured almost simultaneously, but tseconds later, at vehicle 50, which we will call the “rover” and willdesignate by a subscript r. The time-interval t represents theso-far-unknown departure from exact synchronization of the two samplingclocks (452, 552), plus any difference between the time-delays of therespective receivers (43, 53).

[0094] The two-dimensional, horizontal, position coordinates (x,y) ofthe rover with respect to the base, and the epoch offset, t, aredetermined by computing an “ambiguity function” from these measurements,and finding the maximum of this function. This computational method ismodeled on those disclosed in the Counselman '203 patent and in theearlier article entitled “Miniature interferometer terminals for earthsurveying: ambiguity and multipath with GPS,” by C. C. Counselman IIIand S. A. Gourevitch, appearing in IEEE Transactions on Geoscience andRemote Sensing, vol. GE-19, pp. 244-252, October 1981.

[0095] In the following formulas, all positions including those of alltransmitters 30 are expressed in Cartesian coordinates (x, y) withorigin at the known “base” position. Phase is defined to be anincreasing function of time, such that the phase of a carrier wavedecreases with increasing distance from the transmitter.

[0096] The measured carrier phases from the two receivers aredifferenced for transmitter, j, where j is an index that ranges over alltransmitters observed by both receivers: θ^(j) = θ_(r)^(j) − θ_(b)^(j)

[0097] If a transmitter was observed at just one receiver, it isdisregarded. The set of transmitters used is also limited to thoselocated within about 50 km of both receivers, in order to minimizeskywave interference. However, during daytime, powerful (about 10 kW ormore) stations as far away as about 100 km are useful. A list of theFCC-assigned carrier frequencies, transmitted powers, details of antennatowers, and position coordinates of all AM broadcast transmitters withina user-chosen radius of a user-chosen position is conveniently obtainedfrom the FCC's license data base via the Internet at the URL<http://www.fcc.gov/mmb/asd/amq.html#sprung5>.

[0098] A trial set of values {circumflex over (x)}, ŷ, and {circumflexover (t)} of the unknowns x, y, and t is now chosen from within thethree-dimensional (x, y, and t) search “volume” or “space” that we shalldefine below. This volume encompasses all reasonably possible values ofthe unknowns. A three-dimensional grid of trial values filling thisvolume will be tried. From the set of trial values a theoretical phasedifference

{circumflex over (θ)}^(J)({circumflex over (x)},ŷ,{circumflex over(t)})={circumflex over (θ)}_(r) ^(J)({circumflex over (x)},ŷ,{circumflexover (t)})−{circumflex over (θ)}_(b) ^(J)

[0099] is computed for each transmitters j, where${{\hat{\theta}}_{r}^{j}\left( {\hat{x},\hat{y},\hat{t}} \right)} = {{{- \frac{1}{K_{b}^{j}}}\sqrt{\left( {\hat{x} - x^{j}} \right)^{2} + \left( {\hat{y} - y^{j}} \right)^{2}}} + {\omega_{b}^{j}\hat{t}}}$

[0100] and${\hat{\theta}}_{b}^{j} = {{- \frac{1}{K_{b}^{j}}}{\sqrt{\left( x^{j} \right)^{2} + \left( y^{j} \right)^{2}}.}}$

[0101] In the above formulas, ω_(b) ^(J) is the radian frequency oftransmitter j as observed by the base receiver. By radian frequency wemean 2π times the frequency in Hz.$K_{b}^{j} = \frac{c}{\omega_{b}^{j}}$

[0102] is the wavenumber of transmitter j where c is the speed of light.If more accurate information on the actual wavenumber of the ground-wavewithin the region of interest is available, it should be used here.

[0103] Notice that the so-called “theoretical” phase difference{circumflex over (θ)}^(J)({circumflex over (x)}, ŷ, {circumflex over(t)}) depends on a measured frequency.

[0104] If and when the trial values ({circumflex over (x)}, ŷ,{circumflex over (t)}) equal the actual, true, but so far unknown valuesof (x, y, t), and if errors of measurement are neglected, then thetheoretical phase difference {circumflex over (θ)}^(j)({circumflex over(x)}, ŷ, {circumflex over (t)}) will equal the measured phase differenceθ^(J)=θ_(r) ^(J)−θ_(b) ^(J), modulo 2π that is, the theoreticallycomputed and the actually measured phase difference will differ by aninteger number of cycles. This integer represents the phase ambiguity.

[0105] The ambiguity function is computed from the theoretical and theactually measured phase differences as follows:${R\left( {\hat{x},\hat{y},\hat{t}} \right)} = {\sum\limits_{i = 1}^{J}\quad {W_{r}^{j}{{\cos \left( {\theta^{j} - {{\hat{\theta}}^{j}\left( {\hat{x},\hat{y},\hat{t}} \right)}} \right)}.}}}$

[0106] The ambiguity function is a weighted sum, over all includedtransmitters, of cosines of the theoretical-minus-measured phasedifference for each transmitter. Because the cosine function is periodicwith period 2π, the phase ambiguity drops out.

[0107] The weights, W_(r) ^(J), are chosen to give more weight—buthopefully not too much—to stronger stations than to weaker ones. We setthem proportional to the received signal strength, in dB relative to theweakest station included, of transmitter j as observed by the rovingreceiver. The weights are normalized so they sum to one. Thus, in theabsence of measurement errors the ambiguity function will equal one whencorrect trial values are chosen. When the maximum of the ambiguityfunction is found by searching the unknown-parameter space, this maximumvalue indicates the “goodness” of the position determination. At theestimated position and time, the (unweighted) values of the individualcosines indicate the “goodness” of the observations of individualtransmitters. Outliers, or bad observations, should be unweighted andthe maximization repeated.

[0108] To further explain the invention and some alternative embodimentswe now present some actual observations, ambiguity functions actuallycomputed, and instantaneous positioning results obtained in actualpractice with the invention.

[0109] An instantaneous radiopositioning system constructed and operatedin accordance with the invention was demonstrated to work well in actualpractice, in various places in the Boston, Mass., metropolitan area.This actual system was a non-real-time system lacking the telemetrytransmitting and receiving features (transmitter 41 and antenna 44 inFIG. 2; receiver 60 and antenna 54 in FIG. 3) of the preferredembodiment disclosed above. In the actually constructed system allmeasurement data were stored in real time on the computers' hard disks(48, 58). Then after the roving vehicle 50 had returned to the referencestation 40 a temporary Ethernet connection was made between the twocomputers (47, 57); data were copied from one to the other; and thelatter computer performed the ambiguity-resolving, position-determiningcomputation. Also because no telemetry link was available, the samplingclocks (452, 552) in the analog-to-digital converter units (45, 55)plugged into the two (reference station 40 and vehicle 50) computersystems (47, 57) were synchronized by means of a temporary cableconnection between the two systems before the vehicle 50 left thereference station 40.

[0110]FIG. 7

[0111]FIG. 7 is a “ruled-surface” plot of the ambiguity functioncomputed on a grid covering one square kilometer of x and y, for thebest-estimated, virtually correct, value of t. The data used in thiscase are from one instantaneous (0.8-second) observation with the rover50 and base 40 just two meters apart. With such a small separation,errors are rather small.

[0112] The plot shows a towering peak at the correct position of theroving receiver (very near the origin). The peak value of the ambiguityfunction is 0.99. Other local maxima do not exceed 0.4, so the correctposition is clear. Note that negative values of the ambiguity functionare plotted in the same dark gray shade as the lowest positive values.

[0113]FIG. 8

[0114]FIG. 8 is like FIG. 7 but the plot area is increased to 100 squarekilometers. Extending the plot area reveals local maxima as high asalmost 0.6, but the 0.99 maximum near the origin is still unique andquite distinct.

[0115]FIG. 9

[0116]FIG. 9 is like FIG. 8 but the trial value of the synchronizationdeparture, t, is deliberately offset by a small amount. As desired, nopeak above 0.6 occurs in FIG. 9. However, it should be noted that forour currently working system, the ambiguity function is nearly periodicin t with period 100 μs. This periodicity is due to the common factor of10 kHz in all the carrier frequencies observed. The envelope of the 100μs-periodic peaks is slightly modulated due to actual transmitterfrequency deviations from whole-number multiples 10 kHz harmonics, butin practice this modulation does not sufficiently distinguish thecorrect value of t. Therefore the receiver clock offset must be known apriori to within 100 μs of the correct value. In our preferred real-timesystem, the required level of synchronization knowledge is easilyprovided by the telemetry link. In a post real-time system like the onewe have actually built, the problem is more complicated.

[0117] One solution is to observe the modulation sidebands of one ormore transmitters at both receivers, and to crosscorrelate these signalsto determine their group-delay difference. Since the Fourier transformsof the received signals are already available in the computers, theportions of the transform data corresponding to the chosen sidebands maybe cross-multiplied to obtain the cross-power spectrum, whose transformis the crosscorrelation function. Providing, of course, that theobservations overlap in time and frequency, the time of the peak of thecrosscorrelation function indicates the receiver clock offset.

[0118] Another possibility is to measure the frequency, phase, andamplitude of each of several of the strongest peaks in the modulationsidebands of a few strong radio stations at each receiver—just as ifthey were carrier waves. The long correlation times and distinctspectral features that characterize music and voice modulation insure areasonable amount of overlap between the observations at each receiver.If both receivers report observations of some of the same spectralpeaks, these observations can be used in the ambiguity functionprecisely as additional carrier observations would be used. Because thefrequencies of the modulation spectral peaks will be randomly spaced,the observations will not contribute to the 100 μs periodicity andtherefore, t can be unambiguously estimated.

[0119] We chose a simpler approach in our demonstration experiments. Atthe beginning of each experiment, a pulse from a serial port of one ofthe computers was injected into both receivers' antenna terminals. Eachreceiver observed the offset from its own start-of-sampling samplingepoch to this common pulse. The clock offset was computed by subtractingthese observations. Subsequent values of the clock offset were predictedwell within the required accuracy by using the ratio of the observedfrequencies of a particular transmitter at each receiver to indicate theratio of the rates of the two clocks.

[0120] It is not practical to search every position on earth for themaximum of the ambiguity function. In GPS positioning, this problem isusually solved by centering the ambiguity-function search on theC/A-code-based position estimate. For AM navigation, other possibilitiesexist. Because of the close proximity of the transmitters, the receivedpower observations can be used to initialize the search. We have nottested this method yet. We simply search a square kilometer areacentered on the base station position. The receiver clock offset, t, issearched over a 100 μs window centered on the a priori estimate. We usea step size in x, y, and t that is ten percent of the shortestwavelength, or shortest period, in the AM band.

[0121] In the following figures we present results from demonstrationexperiments in which position was determined by maximizing the ambiguityfunction at each and every epoch, independent of all other epochs.

[0122] In one experiment the base receiver was placed at a GPS-surveyedposition in the driveway of co-inventor Counselman's home. The rover wasplaced on a teacart and rolled to three waypoints in a nearby street.For comparison with the AM-broadcast-based, instantaneous-positioningresults, the distances and directions of the waypoints were determinedby means of a tape-measure and the directions of shadows of a pencil,cast by the sun. (We estimate that the latter survey was uncertain by afew meters.)

[0123]FIG. 10

[0124]FIG. 10 is a scatter plot of all of the positions determined inthis experiment. The diamonds, plotted with a line connecting them, showthe rover positions determined by maximizing the ambiguity functionindependently at each 5-second observation epoch. Tight clusters ofoverlapping diamonds appear where the rover stopped at each waypoint.The waypoint positions determined by the tape-and-shadow survey aremarked by gray squares. The diamond clusters are at most five metersfrom the squares. Five meters is about 2.7% of the shortest carrierwavelength observed.

[0125]FIG. 11

[0126]FIG. 11 shows the same positioning results plotted versus time.The AM-broadcast-based positions determined independently every 5seconds are plotted with diamonds for x, the East coordinate, and smallsquares for y, the North coordinate. The tape-and-shadow-determinedwaypoint coordinates are plotted as horizontal lines with steps at theapproximate times when the rover was rolled from one waypoint to thenext.

[0127]FIG. 12

[0128]FIG. 12 shows the values of all the individual cosine terms(unweighted) in the maximized ambiguity functions for the first half ofthis experiment. A different plotting symbol and/or a different shade ofgray is used for each of the twenty AM-broadcast transmitters used.(Twenty is a limit of our present plotting software. We have used morethan thirty greater-Boston-area AM-broadcast stations in otherexperiments. We have also used as few as six, and still obtained aunique, correct, position-determination by maximizing the ambiguityfunction.) The frequencies of these transmitters, in kHz, are given inthe legend at the right side of the plot. If there were no errors ofobservation, all of the cosine values would be exactly equal to one. Infact, all are greater than 0.982, and most are greater than 0.998.

[0129] The distance-error equivalent of an individual cosine term is${\frac{\arccos ({val})}{2\pi}\frac{c}{f}},$

[0130] in which val is the value of the term, c is the speed of light,and f is the carrier frequency of the radio station. Thus, for example,the smallest cosine value of 0.982 corresponds to a distance of aboutfive meters.

[0131]FIG. 13

[0132]FIG. 13 shows results from a longer-distance experiment that weconducted at Hanscom Air Force Base in Mass. The base receiver was leftin a parking lot while the rover was driven to four waypoints in theback of a pickup truck. The receiver was removed from the truck at eachwaypoint to see how badly the truck perturbed the positioning results.FIG. 13 shows the rover positions determined by maximizing the ambiguityfunction independently at every 5-second observation epoch, not justwhen the receiver was out the truck. The position of the truck was alsotracked with a GPS receiver. The GPS receiver was aided by differential(“DGPS”) corrections from a station in Boston. FIG. 13 shows thepositions determined by both the AM-broadcast and the DGPS tracking. TheGPS receiver adaptively controlled its own sampling interval, so itsepochs were not synchronized with the AM-broadcast positioning epochs.Even so, the plot clearly shows that the AM-broadcast instantaneouspositioning and the GPS tracking results agree very well.

[0133]FIG. 14

[0134]FIG. 14 shows the same positioning results plotted versus time.The AM-broadcast-based, instantaneous position determinations areplotted with diamonds for x, the East coordinate, and small squares fory, the North coordinate. The DGPS-determined waypoint coordinates areplotted as horizontal lines with steps at the approximate times when therover was driven from one waypoint to the next. In FIG. 14 it ispossible to see how the roving receiver was removed from the truckshortly after arrival at each waypoint, set down on the waypoint a fewmeters from the truck, left stationary for a minute or two, then placedback in the truck prior to departure for the next waypoint. Nosignificant positioning glitch occurs when the AM-broadcast receiver washandled, and no significant error appears due to proximity of the truck.

[0135] These observations suggest that AM-broadcast-based instantaneouspositioning should work in the vicinity of other electrically-conductingbodies, as well. Because AM-broadcast-band signals (unlike the muchshorter-wavelength signals of, say, GPS) penetrate houses and manybuilding materials, instantaneous positioning in accordance with thepresent invention appears feasible indoors.

[0136] A problem with indoor positioning is that many of the conductorsfound there, such as pipes and wiring, may be long enough to be resonantwithin the AM broadcast band. A resonant wave-scatterer can cause alarge phase perturbation for a carrier-wave near its resonant frequency.In such a situation, our instantaneous-positioning technique involvingmaximization of an ambiguity function has several important advantages.Perhaps the most important is that the technique is instantaneous, sothat the ability to determine position at a given time does not dependon having maintained continuous phase-tracking of all stations'carrier-waves, with no dropouts, losses of lock, or cycle-slips, in thepast. Another major advantage of the invention is that it can exploitpractically every signal in the band, including signals much too weak tolisten to. After the ambiguity function is maximized, discordantobservations, i.e., those having cosine values significantly less thanone, can be downweighted or deleted, and the maximization repeated.

[0137] Replacing the cosine function, cos θ, in the formula for theambiguity function, with a flat-bottomed function having the same 2πperiodicity causes discordant observations to be downweightedautomatically. Such a flat-bottomed 2π-periodic function is$\left( {\frac{1}{2} + {\frac{1}{2}\cos \quad \theta}} \right)^{n},$

[0138] in which the exponent n is an integer greater than 1.

[0139]FIG. 15

[0140]FIG. 15 shows the periodic function$\left( {\frac{1}{2} + {\frac{1}{2}\cos \quad \theta}} \right)^{n}$

[0141] plotted versus θ, for values of θ from −3π to +3π (through three2π cycles of the function), and for three values of n: n=1, n=5, andn=25. The heaviest curve represents the function with n=1; a somewhatlighter curve represents the function with n=5; and the thinnest curverepresents the function with n=25. The general trend is that, as nincreases, the curve becomes more narrowly peaked at θ= . . . , −2π, 0,2π, 4π, . . . , and develops wider, flatter bottoms in-between.

[0142] With n=1, the periodic function of θ is${\frac{1}{2} + {\frac{1}{2}\cos \quad \theta}},$

[0143] which is just a half-sized, biased version of cos θ. Substitutingthis function for cos θ in the ambiguity function has no effect at allon the position estimate, i.e., the position of the maximum of theambiguity function.

[0144] With increasing values of n, the value of the periodic function$\left( {\frac{1}{2} + {\frac{1}{2}\cos \quad \theta}} \right)^{n}$

[0145] becomes more and more sensitive to a small departure of θ fromany of the periodic values . . . , −2π, 0, 2π, 4π, . . . , but less andless sensitive to a value of θ far from one of these periodic values.The effect of increasing n is therefore to make the position estimateless sensitive to observations with gross errors.

[0146] In the initial search for the maximum of an ambiguity functionusing this substitute function, n should be set equal to one. Then thevalue of n should be incremented and the ambiguity function should bere-maximized. The value of n should be incremented again and theambiguity function should be maximized again, repeatedly, until theposition estimate stabilizes or until the value of n exceeds 25,whichever occurs first. When n=25, the ambiguity function hassubstantially lost any sensitivity to a phase-difference observationdiffering from its theoretical counterpart by more than a substantialfraction of a radian at the ambiguity-function-maximizing position.However, the stopping value of n=25 is a somewhat arbitrary choice, andthe practitioner may wish to experiment with different limits indifferent situations.

[0147] Making simultaneous observations of a number of transmitters thatis greater than the minimum number required to determine positionuniquely; looking for inconsistency between individual observations andtheoretical expectations based on other present and past observations;and downweighting or discarding discordant observations, is the basis ofa variety of so-called Receiver Autonomous Integrity Monitoring (RAIM)schemes that have been developed for GPS and related navigationreceivers and systems. Some such schemes may be adapted advantageouslyto the present invention. The present invention is suited to suchschemes better than most or all prior-art AM-broadcast-band-basedpositioning techniques because the present invention involves receivingand processing the entire band, not just selected signals.

[0148] A skilled practitioner will appreciate that the present inventionis not limited to using the 530- to 1700-kHz band of frequencies. Theinvention is applicable to a wide variety of frequencies and types ofsignals, and different ones will be preferable in different situations.For example, lower-frequency signals travel great distances byground-wave with less attenuation, so they are better suited forlonger-distance navigation. Higher-frequency signals traveling byline-of-sight direct paths may be used to obtain finer accuracy inpositioning within a smaller region. An example of the latter signalsmight be FM-broadcast-band signals.

[0149] An important aspect of the present invention is that a compositesignal simultaneously including signals from a plurality of transmittersis formed by the receiver and converted from analog to digital formbefore processing to derive phase information, related to the receiver'sposition, for the signals received from each of the plurality oftransmitters. Prior-art techniques favor a multi-channel approach inwhich signals received from different transmitters are separated andprocessed in different, dedicated, channels. A disadvantage of themultichannel approach is that different channels may introduce differentphase or delay shifts, or “interchannel bias,” that corrupts theposition determination.

[0150] The present invention may appear disadvantageous because itrequires digitizing a bandwidth much greater than that of one signal, infact much greater than the sum of all the bandwidths of all the signalsused to determine a position. This disadvantage is mitigated somewhat bythe efficiency of the FFT. FFT processing of a wide-bandwidth compositeis less feasible in a system requiring continuous tracking, than in aninstantaneous-positioning system such as ours. In aninstantaneous-positioning system it is not necessary for the FFTprocessing to keep up with continuous, real-time, raw-data acquisition.A burst of samples may be taken, then processed more or less at leisure.

[0151] The fact that the present invention preferably utilizes a largenumber of different signals—from every transmitter available withinground-wave range—might seem a disadvantage because using more signalsimplies using at least some much weaker signals. It is more difficult totrack a weak signal without losing lock and/or dropping or slippingcycles. But really there is no such disadvantage, because the presentinvention does not require tracking. Using a sufficient number ofdifferent signals, with a substantial variety of different frequencies,enables position to be determined instantaneously, with no need fortracking, although of course tracking can be combined with instantaneouspositioning (and we have done so, in experiments).

[0152]FIG. 16

[0153]FIG. 16 shows a repeater system 100 enabling radiopositioningantenna 42 and receiver 43 to be located away from theiranalog-to-digital converter 451 and the remainder of the associatedcomputer system (not drawn here, but see FIG. 2 or FIG. 3).AM-broadcast-band signals received by antenna 42 and amplified andfiltered in receiver 43 are applied to modulator 101 where they arecombined with a repeater carrier-wave generated by carrier generator102. The result is a modulated carrier which is transmitted by repeatertransmitter 103 via repeater transmitting antenna 104.

[0154] A signal 105 radiated by antenna 104 and sensed by repeaterreceiving antenna 106 is applied to repeater-system receiver 107 whoseoutput is demodulated by demodulator 108 by reference to a carrier-wavegenerated by carrier generator 109. The demodulated output ofdemodulator 108 is applied to analog-to-digital converter 451 and theremainder of the associated computer system as shown in FIG. 2.

[0155] The repeating transmitter subsystem comprising modulator 101,carrier oscillator 102, transmitter 103, and antenna 104 is a“bent-pipe” repeater. It simply repeats, at a different radio frequency,what receiver 43 hears. What emerges from repeater demodulator 108 is areplica of the output of receiver 43, with hopefully not much noise anddistortion added. There is, of course, an added time-delay. However, any(reasonable) added time-delay is completely absorbed in the estimate ofclock-synchronization-offset in the maximization of the ambiguityfunction, and the position determination is not affected. The repeatersystem 100 may also introduce “delay distortion,” also known as“dispersion,” meaning that its phase shift is not exactly proportionalto frequency. However, any (reasonable) amount of delay distortion canbe calibrated out by means of the phase-calibration signal injected intothe receiver 43 input from calibration generator 63 as shown in FIGS. 4,5, and 6.

[0156] As a skilled practitioner knows, a wide variety of frequencybands and modulation types, including digital types, are available foruse in a transponder system 100.

[0157] Either antenna 42 and receiver 43, or antenna 52 and receiver 53,or both, may be located remotely by use of one or more transpondersystems like that shown in FIG. 16. If more than one transponder systemis used in the same area, they must transmit on different frequenciesand/or with orthogonal modulation to avoid mutual interference.Typically, the transponder frequency or frequencies will be much higherthan AM broadcast frequencies, and the transponder(s) will have limitedrange. However, a short-range transponder is typically much smaller andlighter than a computer system, and requires much less power. These arepowerful advantages for a radiopositioning receiver carried by a person,an animal, or a very small vehicle.

We claim:
 1. A method of instantaneously determining an unknown positionusing radio signals from a plurality of transmitters having widelydistributed and known positions, and a wide range of radio frequencies,comprising: (a) measuring the phases of said radio signals arrivingconcurrently at said unknown position, to obtain a first set ofphase-measurement data; (b) measuring the phases of said radio signalsarriving concurrently at a known reference position, almostsimultaneously with their arrival at said unknown position, to obtain asecond set of phase-measurement data; (c) combining said first andsecond data sets to determine said unknown position.
 2. The invention ofclaim 1, wherein: said radio signals arrive at said unknown position viaground-wave propagation from said plurality of transmitters.
 3. Theinvention of claim 1, wherein: said transmitters operate independently.4. The invention of claim 1, wherein: said radio signals are transmittedwith random phases.
 5. The invention of claim 1, wherein: said first setof phase measurement data refers to a first instant ofconcurrent-signal-arrival at the unknown position, said second set ofphase measurement data refers to a second instant ofconcurrent-signal-arrival time at the reference position, and thedeparture from simultaneity of said first and second instants isdetermined simultaneously with said determination of said unknownposition.
 6. The invention of claim 5, further comprising: resolvingposition ambiguity related to the integer-cycle ambiguity inherent insaid phase measurements.
 7. The method of claim 5 further comprisingforming an ambiguity function of the sets of phase-measurement data in aspatial parameter space and finding the location of the maximum of theambiguity function.
 8. The method of claim 7 wherein the ambiguityfunction is a sum, over all of the transmitters, of a periodic functionof the phase-measurement data.
 9. The method of claim 8 wherein theperiodic function has a period of a cycle of phase.
 10. The method ofclaim 9 wherein the periodic function is a cosine.
 11. The method ofclaim 8 wherein the periodic function is (½+½ cosine θ)^(n) where θ is aphase and n is greater than
 1. 12. The method of claim 1 wherein acomposite of said radio signals, simultaneously including a componentsignal from each of the transmitters, is digitized and then processed tomeasure said phases.
 13. The method of claim 1 further comprisingproviding a repeater system allowing the phases of the signals to bemeasured away from where the signals are received.
 14. The method ofclaim 7 wherein the ambiguity function is${R\left( {\hat{x},\hat{y},\hat{t}} \right)} = {\sum\limits_{j = 1}^{j}{W_{r}^{j}{{\cos \left( {\theta^{j} - {{\hat{\theta}}^{j}\left( {\hat{x},\hat{y},\hat{t}} \right)}} \right)}.}}}$


15. Radiopositioning system for instantaneously determining an unknownposition comprising: a plurality of spatially distributed transmittersat known locations, the transmitters transmitting signals at widelydistributed frequencies; a first receiver located at the unknownposition adapted to receive these signals and to determine their phasesto generate a first set of phase-measurement data; a second receiverlocated at a known reference position adapted to receive the samesignals and to determine their phases at the known reference position togenerate a second set of phase-measurement data; and computing apparatusoperating on the first and second sets of phase-measurement data todetermine the unknown position.
 16. The system of claim 15 wherein thecomputing apparatus is programmed to find the location in a parameterspace of the maximum of an ambiguity function of the sets ofphase-measurement data, the location of the maximum being the unknownposition.
 17. The system of claim 16 wherein the ambiguity function is asum, over all of the transmitters, of a periodic function of thephase-measurement data.
 18. The system of claim 17 wherein in theperiodic function has a period of a cycle of phase.
 19. The system ofclaim 18 wherein the periodic function is a cosine function.
 20. Thesystem of claim 18 wherein the periodic function is (½+½ cosine θ)^(n)where θ is a phase and n is greater than
 1. 21. The system of claim 16wherein the ambiguity function is${R\left( {\hat{x},\hat{y},\hat{t}} \right)} = {\sum\limits_{j = 1}^{j}{W_{r}^{j}{{\cos \left( {\theta^{j} - {{\hat{\theta}}^{j}\left( {\hat{x},\hat{y},\hat{t}} \right)}} \right)}.}}}$


22. The system of claim 15 wherein the output of the first and secondreceivers is a composite signal that is digitized for processing todetermine the phases.
 23. The system of claim 15 further including arepeater system allowing the receivers to be spatially remote from thephase determination.
 24. The system of claim 15 wherein the first andsecond receivers receive the signals via ground-wave propagation fromthe transmitters.
 25. The system of claim 15 wherein the transmitterstransmit carrier signals having random phases.
 26. The method of claim5, further comprising determining said unknown position by: evaluating afunction of said first and second sets of phase measurement data and ofa trial value of said unknown position; searching a range of said trialvalues to find an extreme value of said function; and determining saidunknown position from the trial value for which said extreme value isfound.
 27. The invention of claim 26 further comprising downweightingdiscordant members of said first and second sets of phase measurementdata in the evaluation of said function.
 28. A method of instantaneouslydetermining an unknown position, comprising: collecting a composite ofradio signals arriving simultaneously at said position from a pluralityof transmitters having widely distributed and known positions, and awide range of radio frequencies; forming a digital representation ofsaid composite; processing said digital representation to derive a firstdata set representing phases of signals received from each of saidplurality of transmitters; and combining said first data set with asecond data set representing phases of signals received at a knownposition from the same said plurality of transmitters, to determine saidunknown position with respect to said known position.
 29. The method ofclaim 28, wherein processing said digital representation includes:computing a spectrum of said digital representation; and finding peaksin said spectrum; deriving said first set of phase data from said peaks.